Network Model Averaging Prediction for Latent Space Models by K-Fold Edge Cross-Validation

TL;DR

This paper introduces NetMA, a network model averaging method for latent space models that improves link prediction accuracy, especially in small networks with high-dimensional latent spaces, by optimally combining candidate models.

Contribution

The paper proposes a novel model averaging approach for latent space network models, establishing its asymptotic optimality and consistency, and demonstrating superior empirical performance over existing methods.

Findings

NetMA achieves lower prediction loss than simple averaging and model selection.

NetMA outperforms the oracle method in large latent space dimensions.

Empirical results on real networks confirm NetMA's effectiveness in link prediction.

Abstract

In complex systems, networks represent connectivity relationships between nodes through edges. Latent space models are crucial in analyzing network data for tasks like community detection and link prediction due to their interpretability and visualization capabilities. However, when the network size is relatively small, and the true latent space dimension is considerable, the parameters in latent space models may not be estimated very well. To address this issue, we propose a Network Model Averaging (NetMA) method tailored for latent space models with varying dimensions, specifically focusing on link prediction in networks. For both single-layer and multi-layer networks, we first establish the asymptotic optimality of the proposed averaging prediction in the sense of achieving the lowest possible prediction loss. Then we show that when the candidate models contain some correct models, our method assigns all weights to the correct models. Furthermore, we demonstrate the consistency of the NetMA-based weight estimator tending to the optimal weight vector. Extensive simulation studies show that NetMA performs better than simple averaging and model selection methods, and even outperforms the "oracle" method when the real latent space dimension is relatively large. Evaluation on collaboration and virtual event networks further emphasizes the competitiveness of NetMA in link prediction performance.